About the Put-Call Parity Calculator
This put-call parity calculator uses the no-arbitrage relationship between European calls, puts, the underlying stock and a risk-free bond. Enter the stock price, strike, risk-free rate, days to expiration and any dividend yield, then either solve for the fair call price from a put, the fair put from a call, or enter both market prices to check whether they are consistent. It also shows the present value of the strike and the price of the synthetic stock built from the options.
Options students use parity to check homework and understand synthetic positions; traders use it to sanity-check quotes, find the implied forward or dividend, and spot conversions and reversals when a call and put with the same strike and expiry drift out of line.
Parity holds exactly for European options with the same strike and expiration. Discounting uses continuous compounding with a 365-day year, and dividends are modeled as a continuous yield. American options can trade slightly away from parity because of early exercise, and in practice bid-ask spreads, borrowing costs and commissions usually absorb small apparent mispricings.
With the default inputs, the parity-implied price is $5.23. Change any value above to recalculate instantly.
How to use the put-call parity calculator
- 1Choose whether to solve for the call, the put, or check both prices.
- 2Enter the stock price, strike, risk-free rate and days to expiration.
- 3Add a dividend yield if the stock pays dividends before expiry.
- 4Enter the known option price (or both prices in check mode).
- 5Read the parity-implied price, and in check mode the mispricing and arbitrage trade.
Formula and method
Put-call parity says that a long call plus a zero-coupon bond paying the strike K at expiration must cost the same as a long put plus the stock, because both portfolios are worth max(S, K) at expiration. The bond’s value today is K·e^(−rT) with continuous compounding, and the stock is reduced to S·e^(−qT) when it pays a continuous dividend yield q that the option holder does not receive.
Rearranging gives the fair call from a put and vice versa. In check mode the calculator compares the market call with the parity-implied call. If the call is rich, a conversion (sell call, buy put, buy stock) locks in the difference; if it is cheap, a reversal (buy call, sell put, short stock) does. The synthetic stock price C − P + K·e^(−rT) should equal S·e^(−qT).
- C
- European call price
- P
- European put price (same strike and expiry)
- S
- Current stock price
- K
- Strike price
- r
- Continuously compounded risk-free rate
- q
- Continuous dividend yield
- T
- Time to expiration in years (days ÷ 365)
Worked examples
Fair call from a $4 put
With 90 days to expiry at 5%, the $100 strike is worth 100 × e^(−0.05 × 90/365) = $98.77 today. Parity gives C = 4.00 + 100 − 98.77 = $5.23, so a call quoted at $6.50 would look expensive.
Fair put from a call on an out-of-the-money strike
The $55 strike discounted for 60 days at 4.5% is $54.59. The put should be worth C − S + PV(K) = 1.20 − 50 + 54.59 = $5.79.
Checking quotes on a dividend payer
The stock net of its 1.5% dividend yield is worth $199.02, and the $195 strike discounts to $191.82. Parity implies a call of 7.50 + 199.02 − 191.82 = $14.70, so the $15.00 call is about $0.30 rich. A conversion would lock in roughly $30 per contract before costs.
Frequently asked questions
What is the put-call parity formula?+
For European options on a non-dividend stock, C + PV(K) = P + S, where C and P are the call and put prices, S is the stock price and PV(K) is the strike discounted at the risk-free rate. With a dividend yield, the stock is replaced by S·e^(−qT).
Does put-call parity work for American options?+
Not exactly. Early exercise rights make American options worth at least as much as European ones, so parity becomes a range: S − K ≤ C − P ≤ S − PV(K) for non-dividend stocks. For deep in-the-money puts and dividend payers the gap can be noticeable.
What is a synthetic stock position?+
Buying a call and selling a put with the same strike and expiry behaves like owning the stock: you gain dollar for dollar above the strike and lose below it. Its cost is C − P, and adding the present value of the strike makes it comparable with the stock price.
What are conversion and reversal arbitrage?+
A conversion buys the stock, buys a put and sells a call, locking in a riskless position when the call is overpriced. A reversal (reverse conversion) shorts the stock, sells a put and buys a call when the call is underpriced. Market makers run these trades, which keeps parity tight.
Why might quotes violate put-call parity?+
Apparent violations usually come from bid-ask spreads, stale quotes, hard-to-borrow stocks with high short-sale fees, unexpected dividends or early-exercise value in American options. Real riskless arbitrage is rare and fleeting in liquid markets.
Results are estimates for educational purposes and are not financial advice. Rates, fees and terms vary — confirm with your lender or a licensed advisor before making decisions.